A certain movie star's salary for each film she makes consis

Question

A certain movie star's salary for each film she makes consists of a fixed amount, along with a percentage of the gross revenue the film generates. In her last two roles, the star made $32 million on a film that grossed $100 million, and $24 million on a film that grossed $60 million. If the star wants to make at least $40 million on her next film, what is the minimum amount of gross revenue the film must generate?

A $110 million
B $120 million
C $130 million
D $140 million
E $150 million

can't really figure this out. any help would be great thanks!

A $110 million
B $120 million
C $130 million
D $140 million
E $150 million

Bunuel · Accepted Answer

Basically we have following linear relationship: Salary={Percent}*{Revenue from the film}+{Fixed amount} -->  S=PR+F  (the same as  y=ax+b ).

Given:  32=100P+F  and  24=60P+F . Question: if  S\geq{40}  then  R_{min}=?

Solving:  32=100P+F  and  24=60P+F  --> subtract 2 from 1 -->  8=40P  -->  P=0.2  (so she gets 20% of the revenue) -->  F=12 , so fixed amount is $12 million. So the formula for calculating star's salary is:  S=0.2R+12 .

We want  S=0.2R+12\geq{40}  -->  R\geq{140}  --> so  R_{min}=140 , if the star wants to make at least $40 million on her next film, the film must generate minimum $140 million of gross revenue.

Answer: D.

Hope it's clear.

gsrdeepak · Answer

answer is D.
Let x be fixed income
Let y be the % of variable income.
x+(y/100)*100 = 32
x+(y/100)*60 = 24
so we get x = 12 and y = 20%
then 
x+0.2(required revenue)= 40. we get required revenue = 140 million dollars

azule45 · Answer

i figured it out as so:

a $60 million dollar gross = $24 million
and
a $100 million dollar gross = $32million

we can notice that the difference between the $100 million and $60 million is equal to $40 million. this $40 million equates to an $8 million salary ($32 - $24).

since we want $40 million in salary, we can add the $8 million difference to the $32 million. if we do that, we also need to add the $40 million difference ($100 - $60) to the $100 million. this gives us $140 million. our answer should be $140 million.

does this sound clear?

vwjetty · Answer

awesome explanation guys. thanks.

mun23 · Answer

Really awesome explanation.................

jlgdr · Answer

Movie star earned 8 million more in salary with an increase in 40 movie. That is a ratio of 5 times Therefore in order to gain 40 mil she needs an increase of 8 million, which will correspond to an increase in (8*5 = 40 million) in movie Thus 140 is your best choice Hope it helps Cheers J

pacifist85 · Answer

I used sort of a longer approach and it took me almost 4 minutes to solve... But, for those that can calculate fast and don't have to correct calculation mistakes I guess it wouldn't be a problem:

Z is the fixed amount, x/100 the percentage of the revenue she gets and R the revenue of the film. So:
 Z+  \frac{x}{100}   * 100 = 32 , and

Z+  \frac{x}{100}   * 60 = 24

We subtract the second equation from the first one which leads to:
 \frac{2x}{5}   = 8

2x = 40

x = 20 . So we have the % she earns from the revenue of the film.

We replaxe x for 20 in one of our equations:
 Z+  \frac{x}{100}   * 100 = 32

Z+  \frac{20}{100}   * 100 = 32

Z = 12 , So, we have the fixed amount.

Now, we know that she wants to get 40 on the next film. So,
 12 +   \frac{20}{100}  *R = 40

12+0.2R = 40

0.2R = 28

R = 140 .

So,  ANS D .

EMPOWERgmatRichC · Answer

Hi All,

This question involves what's called "system math", which is an algebra concept. We need to translate the given prompt into a couple of algebra equations, then solve.

We're told that a total is based on a fixed amount + a percentage of a gross. From the two roles, we can create the following equations:

X = fixed amount 
Y = % of the gross

X + Y% of (100 million) = 32 million 
X + Y% of (60 million) = 24 million

We now have a "system" of equations (2 variables with 2 equations, so we CAN solve for X and Y).

Subtracting the second equation from the first gives us…

Y% of (40 million) = 8 million 
Y% = 8/40 = 1/5 = 20% 
Y = 20

Plugging back into either equation, we get…

X+ 20% of (100 million) = 32 million 
X = 12 million

With the value of X and Y, we can now answer the question: To make at least 40 million, the minimum gross revenue must be…

12 million + 20% of (Z) = 40 million 
20% of (Z) = 28 million 
Z = 140 million

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

BrentGMATPrepNow · Answer

Let F = the fixed amount the star receives for a movie
Let p = the percentage of the gross revenue the star receives for a movie

The star made $32 million on a film that grossed $100 million   
So, we can write:  F + (p/100)(100) = 32

The star made $24 million on a film that grossed $60 million  
So, we can write:  F + (p/100)(60) = 24

We now have: 
 F + (p/100)(100) = 32 
 F + (p/100)(60) = 24

Subtract the bottom equation from the top equation to get: (p/100)(100) - (p/100)(60) = 8
Factor to get: (p/100)  = 8
Simplify to get: (p/100)  = 8
Multiply both sides by 100 to get: 40p = 800
Solve: p = 20

Now that we know the value of p, we can find the value of F
Take  F + (p/100)(100) = 32  and replace p with 20 to get: F + (20/100)(100) = 32
Simplify: F + 20 = 32
So, F = 12

So, the star receives 12 million (fixed) PLUS 20% of the gross revenue

If the star wants to make at least $40 million on her next film, what is the minimum amount of gross revenue the film must generate?   
Let x = gross revenue the film must generate
We can write: 12 + 20% of x = 40
Rewrite as: 12 + 0.2x = 40
Subtract 12 from both sides: 0.2x = 28
Solve: x = 140 (million)

Answer: D

Cheers,
Brent

ScottTargetTestPrep · Answer

We can let x = the fixed amount, in millions, the movie star receives and n/100 = the percentage of the gross revenue from the film that she receives. Therefore, we can create the equations:

32 = x + n/100(100)

32 = x + n

32 - n = x

and

24 = x + n/100(60)

24 = x + 3n/5

Substituting, we have:

24 = 32 - n + 3n/5

-8 = -2n/5

-40 = -2n

20 = n

So x is 32 - 20 = 12.

Thus, we see that she earns a fixed amount of $12 million and 20% of the film’s gross revenue.

Let’s determine the gross revenue for a film that allows the movie star to earn 40 million.

40 = 12 + (1/5)(m)

28 = m/5

140 = m

Answer: D

hero_with_1000_faces · Answer

putting equations with 100 as denominator will be time consuming. the best way is

F + 100y = 32
F + 60y = 24

Subtract both you get: 40y = 8 therefore y = 1/5

original equation:
F + 20 = 32
hence, F = 12
atleast 40 needed, so 40 - Fixed = 28

D 140 * 1/5 = 28

Done!

Manasvi1 · Answer

We can see that,
The movie star makes $32 million on $100 million gross revenue
 And,
 $24 million on $60 million gross revenue

We see, 
If gross revenue decreases $40 million, the amount movie star makes decreases by $8 million
 
So, if the amount movie star makes, increases by $8 million(40 - 32) ,
Then,
gross revenue increases by $40 million

So, Total gross revenue= $100 + $40 = $140
  OA (D)

vinayakjjw · Answer

How do we know that she makes a constant % from gross revenues.?

We know she gets a fixed pay and the variable pay. But is it right to assume that the variable pay % per movie is the same?

GMATGuruNY · Answer

Let:
y = the movie's star salary
m = the movie's star's percentage of the gross revenue
x = the gross revenue
b = the fixed amount included in the movie star's salary

Since the movie star's salary consists of her percentage of the gross revenue plus the fixed amount, the result is the following equation:
y = mx + b
This is the EQUATION OF A LINE, where x = the gross revenue and y = the movie star's salary.

On a film that grossed $60 million, the star made $24 million.
On a film that grossed $100 million, the star made $32 million. 
In the other words, the following points are on the line above:
(60, 24)
(100, 32)

These two points indicates that the line has the following SLOPE:
The gross revenue increases by $40 million (here, from $60 million to $100 million) for every $8 million increase in the star's salary (here, from $24 million to $32 million).

If the star wants to make at least $40 million on her next film, what is the minimum amount of gross revenue the film must generate? 
In accordance with the slope of the line:
For the star's salary to increase by another $8 million (from $32 million to $40 million), the gross revenue must increase by another $40 million (from $100 million to $140 million).
Thus, the gross required for a $40 million salary = $140 million.

D

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A certain movie star's salary for each film she makes consis

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A certain movie star's salary for each film she makes consis

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards